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Quiz 2 for STA 100: Probability and Statistics - Prof. William Thistleton, Exams of Data Analysis & Statistical Methods

State University of New York Polytechnic - Utica-RomeData Analysis & Statistical Methods
Prof. William Thistleton

A statistics quiz for sta 100, including 10 questions on topics such as normal distributions, confidence intervals, binomial random variables, and hypothesis testing. Students are expected to use their textbook, notes, and a calculator to answer the questions, which cover calculating probabilities, means, standard deviations, and confidence intervals.

Typology: Exams

Pre 2010

Uploaded on 08/09/2009

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koofers-user-ics 🇺🇸

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STA 100 Quiz 2 13 November, 2003
Prof. Thistleton
I understand that this quiz may be done with our textbook, my notes, and a calculator. I received
no help from any individual, I did not discuss the the exam with anyone, and the work which follows
is entirely my own.
I also understand that the due date for the quiz is November 18th during class and that late papers
will not be accepted.
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Download Quiz 2 for STA 100: Probability and Statistics - Prof. William Thistleton and more Exams Data Analysis & Statistical Methods in PDF only on Docsity!

STA 100 Quiz 2 13 November, 2003 Prof. Thistleton

I understand that this quiz maybe done with our textbook, mynotes, and a calculator. I received no help from anyindividual, I did not discuss the the exam with anyone, and the work which follows is entirelymyown.

I also understand that the due date for the quiz is November 18th during class and that late papers will not be accepted.

signed date

  1. What percentage of the area under a normal curve lies between μ − σ and μ + 2σ?
  2. A population of weights is normallydistributed with mean μ = 5 lbs and standard deviation σ = 3 lbs. (In our notation from class, the distribution is N (μ = 5, σ^2 = 9)). What proportion of weights is between 4 and 7?
  3. Suppose a population is distributed normallywith mean μ and standard deviation σ = 3. If the proportion of data above 10 is 0.2005 (20.05%), what is the mean of the population?
  4. The number of steaks (a discrete quantity) sold at a certain restaurant on a Friday night is approximatelynormallydistributed with mean μ = 30 and standard deviation σ = 10. What is the probabilitythat the restaurant will run out of steaks if it has 50 in its freezer?
  1. You want to determine whether a coin is fair or not. You have been told that it is, indeed fair.

(a) Calculate the probabilityof obtaining 12 heads on 20 tosses with a fair coin using the formula for a binomial random variable.

(b) Calculate the same probabilityusing the normal approximation to the binomial distri- bution.

(c) Being patient, you tossed the coin 1000 times and obtained 550 heads. What is the probabilityof obtaining 550 or more heads with a fair coin? Are you lead to believe that the coin is fair?

  1. A population is normallydistributed. If you obtain the data n = 121 and s = 35

(a) Calculate a 95% confidence interval for the population standard deviation using the χ^2 distribution

(b) (5 points extra credit) Use the large sample approximation to calculate the same confi- dence interval. (i.e. You will use the Z table).

  1. A population of test scores is normallydistributed with a mean of 500 and a standard deviation of 100.

(a) Calculate the probabilitythat a randomlyselected individual from this population will have a score greater than 550 points.

(b) Calculate the probabilitythat a simple random sample of size 10 drawn from this pop- ulation will have a mean score greater than 550 points.

(c) Calculate the probabilitythat a simple random sample of size 50 drawn from this pop- ulation will have a mean score greater than 550 points.